Study on the meshing theory of the ring-shaped roller screw mechanism

Based on the structural characteristics of ring-shaped roller screw mechanism (RRSM), helical equations of the screw, roller and nut are derived. Meshing equations at the screw-roller and nut-roller interfaces are developed, which can be used to calculated contact positions of thread teeth. The equations of axial clearances in the RRSM are also derived and zero-clearance design values of the thread thicknesses are given. By comparing the contact positions and clearances obtained from a previously published numerical model, the feasibility of the proposed model is validated. The influence of structural parameters on the meshing characteristics of the RRSM is analyzed. When the nominal radius of the screw is increased or that of the roller is decreased, the contact point at the screw-roller interface will move towards to the tangential-point of pitch circles. The difference between the value of the screw flank angle and that of the screw flank angle has great influence on contact positions. When the values of the nut and roller flank angles are equal, the contact points will lie on the tangential-point of pitch circles and the zero-clearance design value of the thread thickness at the nut-roller interface is equal to the half of the screw pitch. The radius of the roller thread profile has little influence on the zero-clearance design values of thread thickness.